Question

A student in 12th standard commerce stream has to appear for exam in 7 subjects. It is necessary to pass in all the subjects to pass an exam. Certain minimum marks must be obtained to pass in a subject. In how many ways can a student appearing for the exam fail?

Answer 1

A student has to appear for exam in 7 subjects. Certain minimum marks are required to pass in the subject. He fails if he does not reach to the level of minimum marks required in at least one of 7 subjects.

Total combinations in which a student can fail

= ⁷C₁ + ⁷C₂ + ⁷C₃ + ⁷C₄ + ⁷C₅ + ⁷C₆ + ⁷C₇

= 7 + \(\frac{7×6}{2×1}+\frac{7×6×5}{3×2×1}+\frac{7×6×5×4}{4×3×2×1}+\frac{7×6×5×4×3}{5×4×3×2×1}\) + 7 + 1

= 7 + 21 + 35 + 35 + 21 + 7 + 1

= 127